Simulation Study of Single Quantum ChannelBB84 Quantum Key Distribution

Oi-Mean Foong(&), Tang Jung Low, and Kah Wing Hong

Computer and Information Sciences Department,Universiti Teknologi PETRONAS, Bandar Seri Iskandar,

31750 Tronoh, Malaysia{foongoimean,lowtanjung}@utp.edu.my, h.

kahwing@outlook.com

Abstract. With the increasing information being shared online, the vastpotential for cybercrime is a serious issue for individuals and businesses.Quantum key distribution (QKD) provides a way for distribution of secure keybetween two communicating parties. However, the current Quantum KeyDistribution method, BB84 protocol, is prone to several weaknesses. These arePhoton-Number-Splitting (PNS) attack, high Quantum Bit Error Rate (QBER),and low raw key efficiency. Thus, the objectives of this paper are to investigatethe impacts of BB84 protocol towards QBER and raw key efficiencies in singlequantum channel. Experiments were set up using a QKD simulator that wasdeveloped in Java NetBeans. The simulation study has reaffirmed the results ofQBER and raw key efficiencies for the single quantum channel BB84 protocol.

Keywords: Quantum Key Distribution � BB84 � Cryptosystem � QBER � Rawkey efficiencies

1 Introduction

Physicists and computer scientists are working together in pursuing the constructionand realization of quantum computer, which would exploit and harness the quirks ofquantum mechanics to perform certain computations that are much more efficient andscalable fault-tolerant quantum computers [1, 2].

From years of research, quantum computers are found to be theoretically morepowerful than conventional computers for breaking the cryptographic codes that arecurrently used for many aspects particularly monetary transactions and maintaininginformation confidentiality on the World Wide Web [3]. The security of the currentencryption method which is the public key ciphers are based on mathematical calcu-lations that are simple to compute but require an infeasible amount of processing powerand time to invert [4]. The current encryption methods are thus facing multiple chal-lenges from threats due to weak random number generators, advances to computationalpower, new attack strategies and the emergence of quantum computers.

Bennett and Brassard [5] devised the first Quantum Key Distribution protocol in1984, known as the BB84 protocol. BB84 protocol utilizes the principle of uncertaintyformulated by Stephen Wiesner in 1969 [6] and No-Cloning Theorem. However, eventhough BB84 protocol provides theoretically unconditional security, it is prone to

© Springer Nature Singapore Pte Ltd. 2018K.J. Kim et al. (eds.), IT Convergence and Security 2017,Lecture Notes in Electrical Engineering 450,DOI 10.1007/978-981-10-6454-8_21

several weaknesses. These are Photon Number Splitting (PNS) attacks [7], highquantum bit error rate (QBER) and low raw key efficiency [8, 9].

The objective of this work is therefore to improve the average quantum bit errorrate and raw key efficiency. By minimizing the average QBER in the process ofQuantum Key Distribution, an eavesdropper will have a minimal amount of infor-mation and knowledge about the secret key, effectively ensuring QBER to be below thethreshold governed by the two communicating parties (sender and receiver). Byimproving raw key efficiency in the process of Quantum Key Distribution, more bitsgenerated by the sender will be used as the final secret key between the two com-municating parties. Section 2 analyzes the literature review, Sect. 3 introduces thesingle quantum channel model, Sect. 4 discusses the simulation results based on BB84protocol, and lastly, Sect. 5 concludes this paper.

2 Literature Review

This section discusses the fundamental theories of Quantum Mechanics, the QuantumBit Error Rate and Raw Key Efficiency that ensure the confidentiality of the transmittedkey during secret key transmission.

2.1 Fundamental Theories of Quantum Mechanics

Quantum Key Distribution exploits the strange rules of quantum mechanics to achieveunconditional security for two communicating parties. These counter-intuitive behav-iors and properties of quantum mechanics have direct consequences and pose a chal-lenge in the field of quantum cryptography.

In quantum computing, a quantum bit or qubit is the basic unit of quantum infor-mation. It is the quantum analogue to the classical bits in conventional computers.Unlike classical bits which can only represent 1 or 0, quantum mechanics allows thequbit to be in a superposition of both states, thus representing both 1 and 0 at the sametime [10]. As a result, the qubit can be represented as a linear combination of 1j i and 0j i.

uj i ¼ a 1j i þ b 0j i ð1Þ

where a and b are probability amplitudes and can be complex numbers. When the qubitis measured in the standard basis, the probability of outcome 1j i is bj j2 and theprobability of outcome 0j i is aj j2 where

aj j2 þ bj j2¼ 1 ð2Þ

In the application of a Quantum Key Distribution protocol, a photon, which is lightenergy, may be used to represent a qubit for information encoding [11]. Apart fromthat, quantum states present in a quantum system are very frail and unintended mea-surement as well as exposure to the external environment will destroy its superpositionstate. This makes qubit in the quantum system difficult to be controlled and manipulate.This quantum behavior is described as quantum decoherence and it provides anadvantage in detecting eavesdropper in an event of key sharing in QKD. Therefore,

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qubit used in key distribution must be well secluded from the environment to ensure thequantum states are well protected [12].

According to Oraevsky [13], when a quantum computer contains more than onequbit, measurement of states independently is generally not possible as the qubits canbe linked together in such a way that their states become interdependent. This is knownas quantum entanglement and qubits may remain correlated to each other regardless oftheir distances apart. Quantum entanglement can be utilized in QKD where one photonfrom each pair will be distributed between the sender and receiver to produce a ten-tative secret key.

First discovered by Wooters and Zurek [14], the Quantum No-Cloning Theoremeffectively ensures that a qubit of unknown state cannot be replicated, duplicated or cloned.It is a protection mechanism in quantum theory and is one of the essential concepts used inquantum cryptography, specifically inQKD. Copies of quantum states are therefore cannotbe obtained and an eavesdropper cannot replicate quantum information.

The QKD relies on the Heisenberg Uncertainty Principle articulated by WernerHeisenberg [15], a German physicist who states that two properties of an object cannotbe measured at the same time, even in theory. For instance, if a velocity of an atom is tobe measured, the position of the atom cannot be accurately determined. Thus, in QKDapplication, the polarization state of a photon cannot be measured simultaneously bymultiple polarizers without randomizing either of the measurements, resulting ininaccurate results [16].

2.2 Quantum Bit Error Rate (QBER)

The Quantum Bit Error Rate (QBER) is the measurement of the probability or per-centage of error across the quantum channel during key distribution [10]. It is one ofthe key quantities in QKD to evaluate the quality of light transmission in QKD system.The quality of signal transmission can be affected by numerous factors including thepresence of an eavesdropper, the protocol used, disturbance and noise due to theimperfection of components and transmission impairments to the qubits. In simplerterms, QBER is defined as the ratio of error rate to the key rate and contains infor-mation in the presence of eavesdropper and how much this information was compro-mised. The QBER can be calculated as:

QBER ¼ EBmax

ð3Þ

where E is the length of erroneous bits and Bmax is the length of the raw key.In the ideal quantum channel, QBER is equal to zero and any interference by an

eavesdropper will result in an increase in QBER. However, in the practical world,noises and disturbance due to external sources have to be taken into account. Hence, aQBER threshold has to be set to determine the level of privacy for the transmitted key.

2.3 Raw Key Efficiencies

Many experimental and even commercial QKD systems based on the BB84 protocolhave been proposed, which mainly used photons to represent qubits. An inherent

Simulation Study of Single Quantum Channel 161

weakness of such systems is that the photons can be easily absorbed by the channelthus only a small percentage of these photons reach the receiver, the majority will belost in the channel [9]. The qubits received are therefore precious and should not bewasted. In the BB84 scheme, both the sender and receiver may use different basis with50% probability in which case at least half of the received qubits will be discarded,reducing the efficiency of the system significantly. The raw key efficiency can becalculated using Eq. 4.

F ¼ Bmax

Rð4Þ

where Bmax is the length of raw key and R is the length of the original random key.

2.4 Recent Work

In a 2015, Li et. al. proved the importance of randomness in QKD and that the securityof the final secret key will be compromised if some random input bits are known orcontrolled by an eavesdropper during the process of key transmission. The security ofthe BB84 protocol was analyzed against the strong randomness attack where some ofthe random input bits were completely controlled by an eavesdropper. In weak ran-domness attack analysis, the random input bits were partially controlled by an eaves-dropper. Mogos [18] implemented QKD protocol which utilized a four-state systemwith twelve orthogonal states. In the simulation, the average Quantum Ququarts ErrorRate (QQqER) of the four-state system is found to be 68.34% with the absence of anattacker, and 88.94% with the presence of an attacker. Similarly, Senekane et al. [19]demonstrated an optical implementation of three-non-orthogonal states and a total ofsix states for a QKD protocol where the proposed protocol achieved a higher securitymargin, heightened eavesdropper detections and an improved symmetry. In 2016, Mafu[20] investigated the security proof for QKD protocol which utilizes the quantumentanglement. A simple security proof was proposed where an eavesdropper can onlyguess the output state with a probability that will ensure that the eavesdropper may notobtain more than half of the classical Shannon information regardless of the statetransmitted by the sender.

3 Single Quantum Channel Model

This section discusses the existing single quantum channel key distribution model,known as the BB84 protocol.

3.1 BB84 Protocol Model

In BB84 protocol, both sender and receiver, conventionally named Alice and Bob, willeach possess a dedicated QKD device with a single quantum channel capable oftransmitting polarized photon and a classical channel for bases comparison andtransmission of encrypted text.

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Subsequently, an additional quantum channel will be proposed in next phase of thisresearch work and integrated into the single Quantum Key Distribution Model as a newmethod to improve QBER and raw key efficiencies as shown in Fig. 1.

3.2 BB84 Algorithm

The BB84 protocol includes two bases i.e. rectilinear base and diagonal base while thepolarization state of a photon is used to represent each bit value. The 90° and 135°polarization states are used to represent the binary 1 while 0° and 45° polarizationstates are used to represent the binary 0. The essential secret key sharing phases of theBB84 protocol pseudo codes are as shown in the following:

Fig. 1. Single-QKD model and the proposed quantum channel

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3.3 Simulation Tool

To simulate a QKD device, a quantum security system was developed in JavaNetBeans IDE to simulate the process of Quantum Information such as quantumpolarizer and eavesdropping in the quantum channel. The user is able to select thelength of the bit strings and opt to enable eavesdropping in the quantum channel asshown in Fig. 2.

4 Results and Discussions

Simulated data and results on QBER and raw key efficiency based on the singlequantum channel key distribution method are presented in this section based on thesimulation tool. In this simulation, it is assumed that the user possesses a perfectquantum channel without noises or disturbances and a perfect single-photon source.Non-perfect simulation shall be done in next phase of this research work.

4.1 Simulated QBER and Raw Key Efficiencies for BB84 Protocol

In order to calculate Quantum Bit Error Rate, Eq. 3 was used to estimate the probabilityof percentage of error across the quantum channel during key distribution. Figure 3shows 100 simulations on the BB84 protocol to obtain the average QBER based on 200qubits.

Fig. 2. Single-quantum channel simulation interface

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From 100 simulations, the average QBER can be calculated using the followingequation.

�x ¼Pn

i¼1 xin

ð5Þ

where n is the number of simulations and x is the value obtained from each simulation.The average QBER on BB84 protocol was found to be 25% in the presence of an

eavesdropper. In other words, an eavesdropper present in the quantum channel mayhave 25% knowledge on the transmitted key.

From the simulated outcome, the average QBER of the BB84 protocol is consistentwith the findings reported by Nedra Benletaief et al. [21], Mohamed Elbokhari et al.[22] and Di Jin et al. [8].

To determine raw key efficiencies, Eq. 4 was used. 100 simulations on BB84protocol were conducted to measure the average raw key efficiencies based on 200qubits. The simulation results are shown in Fig. 3.

The average raw key efficiencies was calculated to be 50% by Eq. 5. This wasexpected, as at least half of the generated bits will be discarded due to the consequencesof not knowing which bases that Alice chooses to encode the photons. Hence, Bob wasforced to randomly choose 1 of the 2 bases to measure an incoming photon, resulting in50% probability of choosing the correct base. The average raw key efficienciesobtained from this simulation was agreeable to the findings reported by Di Jin [8],Chris Erven et al. [23] and Hoi-Kwong Lo et al. [24].

5 Conclusion

In conclusion, the simulation study has reaffirmed that the results of QBER and raw keyefficiencies are 25% and 50% respectively for the single quantum channel BB84protocol. These simulation results were consistent with the findings reported by otherresearchers.

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1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

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Fig. 3. QBER and raw key efficiency simulation results on BB84 protocol

Simulation Study of Single Quantum Channel 165

For future work, dual quantum channel security model will be proposed as a newmethod to improve Quantum Bit Error Rate (QBER) and raw key efficiencies based onthe single-quantum channel communication model.

Acknowledgment. This research project is funded by the Ministry of Education Malaysia(MOE) Fundamental Research Grant Scheme (Grant No: 0153AB-K42).

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